Acoustic windows such as sonar domes for use in transmitting or receiving acoustic waveform signals in a liquid environment are well known in the art. Typically, the exterior surface of such windows is exposed to a body of free liquid such as an ocean, lake, or tank. The interior surface of such windows conventionally has an at least partially defined chamber filled with water or other liquid. Factors such as structural integrity and insertion loss (the amount of acoustic signal attenuation of sound waves passing through the acoustic window) are considered when constructing acoustic windows. Typical acoustic windows comprising a relatively soft inner core and structural outer skins, or a single layer of essentially homogenous material, generally operate well at lower frequencies, but have significant insertion loss as frequencies increase.